A longitudinal study of the development of rational number concepts and strategies in the middle grades

The purpose of this project was to trace longitudinal changes in rational number knowledge and proportional reasoning among middle-school students; exposing barriers or detours in their journey toward rational number understanding. One hundred two children were interviewed over the course of the study. Children were interviewed once every 3 weeks (approximately nine times per year per child). At the same time, children’s classes were observed approximately twice per week for the duration of the 20-month study. As a result, parallels between classroom instruction and students’ individual problem-solving strategies were developed, providing implications for curriculum, teaching, and individualized instruction. A Hierarchical Linear Model was used to describe the overall change in students’ thinking across the study, and sample students were compared to their (inter)national peers on rational number items from TIMSS and NAEP. Students entered the middle grades with a large repertoire of strategies for making sense of rational number problems. However, by the end of the eighth grade, students’ strategies tended to narrow and focus on inefficient understandings. Results show that instructional focus on Part/Whole fractions, in particular, hampered students’ ability to reason about ratio, rates, and proportional reasoning. The use of large-scale secondary data with which to compare results from this more modest study enhanced the ability of the researchers to make statistical claims about the generalizability of patterns uncovered in children’s fraction and proportional reasoning strategies.